Wave transmission network



May 26, 1942. f w, P, MASQN 2,284,529

WAVE TRANSMISSION NETWORK /A/VE/VTOR W P MASON 2 Sheets-Sheet 2 FIG. /3

May 26,1942. w. P. MASON WAVE TRANSMISSION NETWORK Filed Aug. 4, 1939 Piuma M as, 1942V WAVE TRANSMISSION NETWORK Warren P. Mason, West Orange. N. J., assigner to Bell Telephone Laboratories, Incorporated, New York. N. Y., a corporation of New York Application August 4, 1939, Serial No. 288,287

16 Claims.

This invention relates to wave transmission networks and more particularly to networks adapted to couple loads having different imped-v ances.

An object of the invention is to provide an impedance transforming network suitable for use at high frequencies and capable of transmitting a wide band with uniform ratio of transformation.

Other objects are to control the location and the width of the transmission band in a network of this type.

A further object is to improve the transmission characteristics of such a network when operating between terminal loads which have reactive components.

In accordance with the invention there is provided a wave transmission network adapted to transmit freely a selected band of frequencies with a uniform ratio of impedance transformation for coupling two loads having unequal impedances. The network comprises three sections of transmission line arranged in series-shunt relationship and two end capacitors. Two of the sections of line may be connected in shunt at the ends of the third section. or two sections may be connected in tandem and the third section connecd in shunt at their junction. The end capacitors may be connected both in series, both in shunt or one in series and the other in shunt. They may be made variable for tuning the network to pass the desired band of frequencies, and for making allowance for reactive components associated with the load impedances. The

length of one or more of the line sections may be made variable for controlling the width of the transmission band. Three types of networks are disclosed, namely, high impedance transformers, low impedance transformers and those which have a high impedance on one end and a low impedance on the other.

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawings, of which:

Fig. 1 is a schematic circuit of a high impedance transforming filter in accordance with the invention;

Fig. 2 shows the physical structure of a r work which has the circuit shown in Fig. 1;

Figs. 3 and 4 show equivalent electrical cuits for a section of transmission line;

Fig. 5 shows an alternative structure for i circuit of Fig. 1 in which the r of inductances replaced by a T of inductances;

Fig. 6 shows the mechanical structure for the network of Fig. 5;

Fig. 7 shows the equivalent electrical circuit for the network of Fig. 6;

high impedance on one end and a low impedance on the other end:

Fig. 9 shows a physical structure for the circuit of Fig. 8;

Fig. 10 shows an alternative physical structure for the network of Fig. 9 in which the r of line sections has been replaced by a T structure:

Fig. ll shows the equivalent electrical circuit for the structure of Fig. 10;

Fig. 12 shows the circuit of an impedance transforming'iter having relatively low impedances at both ends;

Fig. 13 shows the mechanical structure for the filter of Fig. 12;

Fig.- 14 shows the equivalent electrical circuit for the network shown in Fig. 13;

Fig. 15 shows an alternative structure for the circuit of Fig. 12 in which the 1r of inductances rep1aced by a T of inductances;

Fig. 16 shows the physical structure for the circuit of Fig. 15;

Fig. 17 shows in more detail the mechanical` structure of the filter of Figs. 5 and 6; and a Fig. 18 is a fragmentary showing of an alternative construction for one of the variable capacitors shown in Fig. 17.

First will be considered the high impedance transformers, that is, those whose terminating impedances are higher than the characteristic impedances of the transmission line sections used in their construction. A transformer of this type may be obtained by using shunt anti-resonant branches at both ends of the network. Fig. 1 shows such a circuit in which the shunt branches are coupled by the series inductance L1 to form a series-shunt type network between the input terminals I, 2 and the output terminals I, I. The values of the component inductances and capacitances are given by the following formulas:

420,20., T (fri-f2) ZoIUz-fi) amil-Wi Y 1 21m-MZ,

2f(fz-f1)Zu in which ZuI is the characteristic impedance at the mid-band frequency at the input end, Zuo represents the same quantity at the output end,

Fig. 8 shows the circuit of a filter having a C0 r2 is the ratio of Zoo to Zul, and f1 is the lower limit and fz the upper limit of the band of frequencies throughout which the transforming lter will transform without loss.

The circuit of -Figgflmay be provided b v the network 'shown schematically in Fig. 2 comprising three sections of uniformtransmission line and two capacitors. The two sections oi line -8 and 8 are short-circuited at their outer ends and at their other ends are connected in shunt at the respective ends of the series line section 1f, and the capacitors I and II are also connected'in shunt at the ends of the series section.' As illustrated. the sections of line are ofthe concentric conductor type. Line section 1, for example, has an outer cylindrical conductor I8 and a concentric inner conductor I4. 'I'he capacitors may be made variable, for the purposes set forth hereinafter. The input connections may be made at the points marked I, 2 and the output connections at the points marked 3, 4

A section of uniform transmission line such as 6, 1 or 8 maybe represented by the series-shunt type network shown diagrammatically in Fig. 3 comprising the two shunt impedance branches ZA, ZA and the interposed series branch ZB. Assuming that the lirie is dissipationless these impedances will have the values given by the following formulas:

zA -jzo ot gf (c) zB :izo sin TZ (7) Where a=V (a w is 21|- times the frequency, l is the length of the line and L and C are respectively the distributed yinductance and the distributed capacitance of the line per unit length.

If the line lengths are less than one-eighth of a wave-length wl 2v 2 :1 l cot 2v wl wlx/LC 0) and sin wlJwa/I (11) Therefore, substituting in Equations 6 and 7,

ZA=ITCT (12) and ZB=7`wlL (13) It follows from this that for a line length of less than an eighth wave-length the simplified lumped electrical representation is as shown in Fig. 4 in which each shunt impedance is a capacitance C1 equal in value to vhalf of the total distributed capacitance of the line section and the series irnpedance is an inductance L1 equal in value to the total distributed inductance of the line. If longer sections are used the values of the impedances in the equivalent circuit may, of course, be found from Formulas 6 and 7. In practice it is found that line lengths less than threesixteenths of a wave-length are usually to be preferred, because the ratio of the useful inthe loads.

as indicated by the arrow The vdistributed mductan'ce L and the distributed capacitance C of a coaxial conductor, per centimeter. are given by the formulas:

where a is the outside diameter of the inner conductor and b is the inside diameter of the outer conductor.

It follows, therefore, from the above analysis 'that by a proper choice of line lengths and ratios of diameters the 1r of line sections in the network of Fig. 2 may be so designed that its equivalent electrical circuit is the same as that shown in Fig. 1. In practice, however, it is usually found desirable not to supply all of the capacitances C: and C3 by the distributed capacitance of the line sections, and to make up the difference by means of the shunt capacitors I0 and II of Fig. 2. These capacitors are preferably made variable, in orderto permit tuning of the lter to move the transmission band slightly in one direction or the other. Also, the values of the capacitances C: and Ca may be reduced somewhat from those calculated in order to allow for negative reactive components which may be associated with the load impedances. If these capacitances are properly adjusted the illter will, in eiIect, be terminated in purely resistive loads and the transmission characteristic will thereby be improved. Making the .capacitors I0 and II variable permits this adjustment to be made more precisely, as it is sometimes dulicult to determine the reactive component of a load prior to its connection to the lter terminals.

Fig. 5 shows another lumped element network circuit which is electrically equivalent to that of Fig. 1. In Fig. 5 the three inductances LA, LB and Lc are formed into a T which replaces the 1r of inductances made up of L1, L: and La in Fig. 1. 'I'he values of the inductances in the T may be found in terms of the inductances in the 1r by applying the following standard conversion formulas:

LLg LAmuffa u@ LzLs o LBL1+L2+L3 (17) LiL: LC LlriLzrI-Ls (18) conductor transmission lines I6, I1 and I 8. Two

of the sections, I6 and I'I, are connected in tandem and thethird section, I8, is short-circuited 2,204,520 at its outerend andai itsother endisconnected in shunt at their iunction. The effective lengthoithe shuntsectioncanbevariedbymoving the annular conducting member il in one direction or the other and thereby short-circuitingthe line Il atthedesiredpoin't.`

Fig. 'I shows the equivalent electrical circuit for the T of line sections shown in Fig'. 6. In addition to the inductances Ls, Lm and Lc the circuit includes the end shunt capacitances 20 and 22 and the capacitance 2i in shunt with Ls. The capacitances 2l and 22 form parts of the capacitanoes Cz and C1, respectively. of Fig. 5. By proper design the capacitance 2l can be made so small that, at the mid-band frequency of the which is the same as that o! Fig. 6 except the shunt capacitor II is replaced by a series capacitor 2l. Pig. ll shows thel equivalent circuit of the T of line sections and the series capacitor 25. The circuit' for the line sections is the same as that given in Fig. 7. 1n Fig. 11 it is seen that there are two extra capacitances, 2l and 22, which are not found in the circuit of Fig. 8. 'I'he effect of the capacitance 2| may filter, its impedance is large compared to that oi the inductance Ls, and therefore 'the eilect of this capacitance may be neglected.

The network of Fig. 6 is completed by the addition of the shunt end capacitors Il and II.. The capacitor In will have a capacitance equal to C1 minus the capacitance 2l. The capacitor I I will have a capacitance equal to C: minus the capacitance 22. In each case allowance should be made for any reactive component which may be associated with the load impedance. As explained above, the capacitors III and Il may be made variable for tuning the illter to pass the desired band. By adjusting the effective length of the line section I6 the width of the transmission band may be controlled.

. Fig. 8 is the circuit of an impedance transforming filter which may be designed to have a high impedance at the input end, represented by terminals I, 2, and a low impedance at the output end, represented by terminals I, 4. The circuit is characterized by an anti-resonant shunt branch comprising C4 and L4 at the input end and a series capacitance Cs at the output end. The values of the component elements may be found from the following formulas:

impedance of the parallel combination of Ls and the capacitance is equal to the former impedance of La alone.

The 1r of inductances consisting of L4, L5 and La in Fig. 8 may be transformed into an equivalent T of inductances by means of the Formulas 16, 17 and 18. The T of inductances may be provided bv the network structure shown in Fig. 10

be allowed for by decreasing the lvalue of Ln until the impedance of the parallel combination of La and the capacitance 2l is the same, at the mid-band frequency, as is the former impedance of La alone. Since the capacitance of the series capacitor 26 isl ordinarily large compared tothe shunt capacitance 22, the principal effect of the latter is to decrease'slightly the ratio of impedance transformation for the filter.

Fig. 12 shows av circuit capable of stepping down from the impedance oi a transmission line to a very low impedance. The filter comprises the 1r of inductances made up of In, Is and La and the series end capacitances Cs and Cv. The values of the component elements may be found from the following formulas:

Fig. 13 shows the physical structure for the circuit of Fig. 12. The network is similar to the one shown in Fig. 9 except that the shunt capacitor I0 has been replaced by the series capacitor 26. The equivalent electrical circuit is given in Fig. 14, which differs from Fig. 12 by including the capacltances 21 and 26, shunting the inductances In and Le, respectively. 'I'he values of these inductances can bedecreased to compensate for the effect of these capacitances,

as explained above in connection with the 'capacitance 2| in Fig. 11.

Fig. l5 shows the alternative circuit for that 0f Fig. 12 employing a T of inductances L10, L11 and L12. The values of these inductances. may

be found from those of the inductances Lv, La

and La by means of the conversion Formulas 16, 17 and 18. The physical structure comprising a T assembly of line sections is shown in Fig. 16. There will be a capacitance in shunt with the central inductance L11 contributed by the distributed capacitance of the line sections I6, I1 and I8 which may be compensated for by an adjustment of the value of L11 as explained above in connection with Fig. 11. The distributed capacitances of the line sections I6 and I1 will also contribute two shunt capacitances appearing effectively in shunt at the outer ends of the in- .ductors Lw and L11 which will slightly modify the transformation ratio of the filter, as already explained in connection with the capacitance 22 in.

Fig. 11.

A `specific example Aofanlimpedance transf forming filter in accordance `with the circuit of Fig. and the structure of4 Fig' 6 will now be considered. The preferred-physical embodiment 'is shown in Fig. 17. It isi assumed that the dii ode 30 having a resistive impedance of 1500 ohms and an effective shunt capacitance of 1 micromicrofarad is to be coupled to a concentric conductor transmission line 3I having a lcharacteristie impedance of 70 ohms. The lower cut-off frequency fi is to be 430 megacycles and the up` 02:2.65 micro-microfarads C3=56.8 micro-microfarads LA=46.3 X -9 henries LB=0.909 x 10 henry Lo= 1.30 X 10 henries As a matterl of convenience in construction the two line sections I1 and I8 are chosen of the same impedance and, therefore, may be constructed with outer conductors of the same inside diameter and inner conductors of the same outside diameter. Furthermore, these two sections are arranged in axial alignment, with a. continuous cylindrical outer conductor 32 and a continuous cylindrical concentric inner conductor 33. The outer conductor 32 has an inside diameter of 2 inches and the inner conductor has an outside diameter of 1.5 inches. The line section I1 has a length of 1 inch and the section I8, which is variable, has a maximum length of about l inch. The inner conductor 33 is supported from the end plate 34 by means of the annular flange 35 to which the conductor is securely attached. Screws such as 35 hold the end plate in place. The conductors are made of aluminum, brass or other metal of good conductivity.

The outer end of the line I8 is short-circuited at the required point by means of the annular metallic member 31 having fastened theretov a number of springs, such as 38 and 39, which contact both the inner and outer conductors. The short-circuiting member 31 may be moved in or out by means 0f the three push rods 40 which are fastened at one end to the member 31 and. at the other end to the disc 4I which is preferably made of insulating material. 'I'he effective length of the line section I8 may therefore be adjusted by sliding the member 31 in or out- For the filter under consideration the effective length of the line I8 is about 0.62 in ch.

At the outer end of the line 4section1|1 is the shunt capacitor I I which has a fixed portion and a variable portion. The fixed portion consists of the capacitance between the end plate 43 of the inner conductor 33 and the annular flange 44 on the end plate 45 of the outer conductor 32. The mica ring 48 serves as a separator, and its high dielectric constant increases the capacitance. The end plate 45 is held in position by means of screws such as 45 which screw into shoulders such as 41 secured to the inside of the outer conductor 32.

` inthe end plate 45 and is locked in adjustment by means ofthe clinch nut 5I inserted in the hole. As the screw 50 is turned by means of the screw-driver slot in its yend the disc 49 is lmoved nearer to or further away from the end plate 43 and the capacitance 'is therebyvaried. Fig.

v18 shows an alternative construction for the variable portion of the capacitor II in which the screw50 extends in the opposite direction and the clinch nut 5I is inserted in a hole in the end plate 43 associated with the inner conductor 33. This screw may be extended, if desired, to proiect through the end plate 34. In this case the variable capacitance is that effective between the disc 49 and the end plate 45.

The line section I5 has a cylindrical outer conductor 53 with an inner diameter of 2 inches and a concentrically positioned inner conductor 54 with an outer diameter of 1,4, inch. The inner end of the inner conductor 54 extends through a hole 55 in the outer conductor 32 and is conductlvely. attached to the inner conductor 33. The inner Venti of the outer conductor 53 is soldered, welded or brazed to the side of the outer conductor 32. 'Ihe outer end of conductor 53 is extended and closed with the end plate 55 to provide/a shielded compartment for the thermionlc device 30 which has a cathode 51, a heater element 58 and a plate 59. The length of the inner conductor 54, measured from the point of attachment to the conductor 33 to the plate 59, is theoretically 3.86 inches but this may be shortened somewhat to allow for the capacitance and inductance associated with the wiring to the tube, or for similar effects.

Electrical connection to the cathode 51 is made through the capacitor 60 which comprises an o uter metal plate 5I`, an inner metal plate 52, a separator 53 and a second separator 54 having a portion which serves as an insulating bushing. The two plates 5I and 62 are held in place by the rivet 55. Connection to the heater element 58 is made through a capacitor 65 having a construction similar to that of the capacitor 50.

The variable capacitor I0 is constituted by the metallic disc 58 attached to the inner conductor 54 near its outer end andy the screw 59 which threads through the clinch nut 10 inserted in the wall of the outer conductor 53. As the screw 59 is turned the spacing between its end and the disc 58 is varied and a variable capacitance is thus provided.

In the filter of Fig. 17, for the dimensions given, the line section I5 will provide an inductance LA of 46.3);(104 henries with a shunt capacitance of 1.06 micro-microfarads at each end. The line section I1 will furnish an inductance Lc of 1.30 109 henries with a shunt capacitance of 2.17 micro-microfarads at each end. The line section I8 provides an inductance LB of 0.909X 10-9 henry shunted by a capacitance of 1.52 micromicrofarads. In the equivalent circuit of Fig. 7, therefore, the capacitance 2| will have a value of 4.75 micro-microfarads. However, at the mid-band frequency this capacitance will have an impedance which is about thirty times the impedance of the inductance LB and therefore the effects of the capacitance 2| may be neglected.

Assuming that the diode 30 has an effective shunt capacitance of 1 micro-microfarad then the capacitance to be supplied by the variable capacitor I will be 2.65-1.061=0.59 mici'o-rnicroiarad The capacitance to be furnished by the capacitor il will be 56.80-2.17=54.63 micro-microfarads For the line sections I1 and I8 the characteristic impedance is 17.3 ohms and for the section I6 it is 166.5 ohms. f

In operation, the filter shown in Fig. 17 can be accurately tuned to pass the desired band of frequencies by manipulating the screws 50 and 69. and the Width of the transmission band may be regulated by sliding the short-circuiting member 31 in or out.

What is claimed is:

1. A wave transmission network for transmitting with substantially uniform ratio of impedance transformation a selected band of frequencies between two loads having unequal impedances comprising three sections of uniform transmission line arranged in series-shunt relationship and two capacitors connected at the respective ends of said arrangement of line sections.

2. A network in accordance with claim 1 in which each of said sections of line has a length equal to less than three-sixteenths of the wavelength corresponding to the upper limit of said band of frequencies.

3. A network in accordance with claim 1 in which two of said sections of line are connected in shunt at the respective ends of the third section.

4. A network in accordance with claim 1 in which two of said sections of line are connected in tandem and the third section is connected in shunt at their junction.

5. A network in accordance with claim 1 in which said capacitors are connected in series.

6. A network in accordance with claim 1 in which one of said capacitors is connected in shunt and the other of said capacitors is connected in series.

7. A network in accordance with claim 1 in which means are provided for varying the effective length of one of said sections of line.

8. A network in accordance with claim 1 in which two of said sections of line are connected in tandem, the third section is connected in shunt at their `junction and said capacitors are connected in shunt.

9. A network in accordance with claim 1 in which two of said sections of line are connected in tandem, the third section is connected in shunt at their junction, said capacitors are connected in shunt and means are provided for varying the effective length of said third section.

10. A network in accordance with claim l in which two of said sections of line are connected in tandem, the third section is connected in shunt at their junction, said capacitors are connected in shunt, means are provided for varying the effective length of said third section and means are provided for varying the capacitances of said capacitors.

1l. A network in accordance with claim 1 in which two of said sections of line are connected in shunt at the respective ends of the third section, one of said capacitors is connected in series and the other of said capacitors is connected in shunt.

12. A network in accordance with claim 1 in lwhich two of said sections of line are connected in shunt at the respective ends of the third section and said capacitors are connected in series.

13. A wave transmission network for transmitting with substantially uniform ratio of impedance transformation a selected band of fre- `quencies between two loads having unequal impedaces comprising a section of uniform transmission line so connected as to permit the transmission of energy from one end to the other, two other sections of uniform transmission line connected with said first-mentioned section of line to form a series-shunt arrangement and two capacitors connected at` the respective ends of said arrangement of the sections.

14. A network in accordance with claim 13 in which said capacitors are connected in shunt.

15. A network in accordance with claim 13 in which one of said capacitors is made variable.

16. A network in accordance with claim 13 in which both of said capacitors are made variable.

WARREN P. MAsoN. 

